I am having an argument with my friend about how a nearly-full soda bottle should be stored in the fridge, with the goal of keeping the soda from going flat (i.e. keeping as much of the gas dissolved in the liquid as possible). Assume the bottle is a standard 2L bottle and its walls are impermeable so this is a purely static problem.
He thinks it doesn't make a difference whether the bottle is standing up vertically or lying flat horizontally. I think that standing up is better. My vague reasoning is that in either case, the plastic surface will feel the same amount of pressure $P$ from the contents; but when the bottle is lying horizontally, the shape of the air has a larger surface area and needs more stuff in it to attain the same pressure (since pressure if force over area).
My statement about the shape of the air is likely true by the isoperimetric inequality (or at least some heuristic which says that among shapes with the same volume, the ones "closer" to a sphere have less surface area), since the air-shape at the top of the bottle in the vertical case is closer to a sphere, than the shape when it is lying horizontally (in this case the air is like a long prism). However I'm not sure it's true that the pressure felt by the plastic is the same in both cases.
Who is right and why?
EDIT: thank you for your explanations. I understand how to answer this in terms of constant volumes now, although it isn't very intuitive to me. I wonder if there is an explanation involving the sum of the forces acting on the surface of the liquid being zero, for both the horizontal and vertical configurations.
Best Answer
The volume of the bottle and the volume of the liquid are the same both ways. By subtraction, the means the gas volume is the same either way. The difference assumes in the question’s reasoning doesn’t exist.
There is more area in the sideways case. That’ll let equilibrium be reached more quickly. But it’ll reach the same equilibrium either way.